Question

find \\(f+g\\), \\(f-g\\), \\(fg\\) and \\(\frac{f}{g}\\). determine the domain for each function.

\\(f(x) = 6x + 1\\), \\(g(x) = x - 3\\)

a. the domain of \\(f+g\\) is \\((-\infty, \infty)\\). (type your answer in interval notation.)
b. the domain of \\(f+g\\) is \\(\\{\quad\\}\\). (use a comma to separate answers as needed.)
c. the domain of \\(f+g\\) is \\(\varnothing\\).

\\((f-g)(x) = 5x + 4\\) (simplify your answer.)

what is the domain of \\(f-g\\)?

a. the domain of \\(f-g\\) is \\(\quad\\). (type your answer in interval notation.)
b. the domain of \\(f-g\\) is \\(\\{\quad\\}\\). (use a comma to separate answers as needed.)
c. the domain of \\(f-g\\) is \\(\varnothing\\).

Explanation:

Calculate the function difference

$$ (f - g)(x) = f(x) - g(x) = (6x + 1) - (x - 3) = 6x + 1 - x + 3 = 5x + 4 $$

Determine the domain of the difference function

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Answer:

• (A) The domain of \(f - g\) is \((-\infty, \infty)\). (Correct answer)
• (B) The domain of \(f - g\) is \(\{\quad\}\).
• (C) The domain of \(f - g\) is \(\varnothing\).